Introduction to traveling waves:
Saved in:
| Main Authors: | , , |
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| Format: | Book |
| Language: | English |
| Published: |
Boca Raton ; London ; New York
CRC Press
2023
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| Edition: | First edition |
| Series: | A Chapman & Hall book
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xiii, 160 Seiten Diagramme |
| ISBN: | 9780367707057 9780367707026 |
Staff View
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| adam_text | Contents Preface Chapter xi 1 ■ Nonlinear traveling waves 1 1.1 TRAVELING WAVES 1 1.2 REACTION-DIFFUSION EQUATIONS 5 1.3 TRAVELING WAVES AS SOLUTIONS OF REACTION-DIFFUSION EQUATIONS 8 1.4 PLANAR WAVES 12 1.5 EXAMPLES OF REACTION-DIFFUSION EQUATIONS 14 1.5.1 Fisher-KPP equation 14 1.5.2 Nagumo equation 18 1.6 OTHER PARTIAL DIFFERENTIAL EQUATIONS THAT SUPPORT WAVES 1.6.1 Chapter 21 Nonlinear diffusion,convection,and higher order derivatives 21 1.6.2 Burgers equation 21 1.6.3 Korteweg-de Vries(KdV) equation 22 2 ■ Systems of Reaction-Diffusion Equations posed on infinite domains 27 2.1 SYSTEMS OF REACTION-DIFFUSION EQUATIONS 27 2.2 EXAMPLES OF REACTION-DIFFUSION SYSTEMS 31 2.2.1 FitzHugh-Nagumo system 31 2.2.2 Population models 34 vii
viii ■ Contents Chapter 3.1 3.2 3.3 3.4 3.5 Chapter 2.2.3 Belousov-Zhabotinski reaction 38 2.2.4 Spread of infection disease 41 2.2.5 The high Lewis number combustion model 42 3 ■ Existence of fronts, pulses, and wavetrains 49 TRAVELING WAVES AS ORBITS IN THE ASSOCIATED DYNAMICAL SYSTEMS 49 DYNAMICAL SYSTEMS APPROACH: EQUILIBRIUM POINTS 53 EXISTENCE OF FRONTS IN FISHER-KPP EQUATION: TRAPPING REGION TECHNIQUE 58 3.3.1 Existence of fronts in Nagumo equation 64 3.3.2 Rotated vector fields and existence of a heteroclinic orbit between A and C for some cփ0 69 EXISTENCE OF FRONTS IN SOLID FUEL COMBUSTION MODEL 71 WAVETRAINS 75 4 ■ Stability of fronts and pulses 83 4.1 STABILITY: INTRODUCTION 83 4.2 A HEURISTIC PRESENTATION OF SPECTRAL STABILITY FOR FRONT AND PULSE TRAVELING WAVE SOLUTIONS 86 4.3 4.2.1 Eigenvalue problem 87 4.2.2 Spectrum and spectral stability 97 LOCATION OF THE POINT SPECTRUM 109 4.3.1 4.3.2 Spectral Energy Estimates 109 Evans function 119 4.3.2.1 Definition of the Evans function 119 4.3.2.2 Gap Lemma 125 4.3.2.3 Evans functioncomputation: scalar equations 126
Contents ■ ix 4.3.2.4 Evans function computation: systems of equations 4.4BEYOND SPECTRAL STABILITY 134 144 Bibliography 149 Index 159
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| adam_txt |
Contents Preface Chapter xi 1 ■ Nonlinear traveling waves 1 1.1 TRAVELING WAVES 1 1.2 REACTION-DIFFUSION EQUATIONS 5 1.3 TRAVELING WAVES AS SOLUTIONS OF REACTION-DIFFUSION EQUATIONS 8 1.4 PLANAR WAVES 12 1.5 EXAMPLES OF REACTION-DIFFUSION EQUATIONS 14 1.5.1 Fisher-KPP equation 14 1.5.2 Nagumo equation 18 1.6 OTHER PARTIAL DIFFERENTIAL EQUATIONS THAT SUPPORT WAVES 1.6.1 Chapter 21 Nonlinear diffusion,convection,and higher order derivatives 21 1.6.2 Burgers equation 21 1.6.3 Korteweg-de Vries(KdV) equation 22 2 ■ Systems of Reaction-Diffusion Equations posed on infinite domains 27 2.1 SYSTEMS OF REACTION-DIFFUSION EQUATIONS 27 2.2 EXAMPLES OF REACTION-DIFFUSION SYSTEMS 31 2.2.1 FitzHugh-Nagumo system 31 2.2.2 Population models 34 vii
viii ■ Contents Chapter 3.1 3.2 3.3 3.4 3.5 Chapter 2.2.3 Belousov-Zhabotinski reaction 38 2.2.4 Spread of infection disease 41 2.2.5 The high Lewis number combustion model 42 3 ■ Existence of fronts, pulses, and wavetrains 49 TRAVELING WAVES AS ORBITS IN THE ASSOCIATED DYNAMICAL SYSTEMS 49 DYNAMICAL SYSTEMS APPROACH: EQUILIBRIUM POINTS 53 EXISTENCE OF FRONTS IN FISHER-KPP EQUATION: TRAPPING REGION TECHNIQUE 58 3.3.1 Existence of fronts in Nagumo equation 64 3.3.2 Rotated vector fields and existence of a heteroclinic orbit between A and C for some cփ0 69 EXISTENCE OF FRONTS IN SOLID FUEL COMBUSTION MODEL 71 WAVETRAINS 75 4 ■ Stability of fronts and pulses 83 4.1 STABILITY: INTRODUCTION 83 4.2 A HEURISTIC PRESENTATION OF SPECTRAL STABILITY FOR FRONT AND PULSE TRAVELING WAVE SOLUTIONS 86 4.3 4.2.1 Eigenvalue problem 87 4.2.2 Spectrum and spectral stability 97 LOCATION OF THE POINT SPECTRUM 109 4.3.1 4.3.2 Spectral Energy Estimates 109 Evans function 119 4.3.2.1 Definition of the Evans function 119 4.3.2.2 Gap Lemma 125 4.3.2.3 Evans functioncomputation: scalar equations 126
Contents ■ ix 4.3.2.4 Evans function computation: systems of equations 4.4BEYOND SPECTRAL STABILITY 134 144 Bibliography 149 Index 159 |
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| illustrated | Not Illustrated |
| index_date | 2024-07-03T21:29:25Z |
| indexdate | 2024-07-10T09:46:31Z |
| institution | BVB |
| isbn | 9780367707057 9780367707026 |
| language | English |
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| spelling | Ghazaryan, Anna R. Verfasser aut Introduction to traveling waves Anna R. Ghazaryan, Miami University, USA, Stéphane Lafortune, College of Charleston, USA, Vahagn Manukian, Miami University, USA First edition Boca Raton ; London ; New York CRC Press 2023 xiii, 160 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier A Chapman & Hall book Dispersion Welle (DE-588)4150202-4 gnd rswk-swf Reaktions-Diffusionsgleichung (DE-588)4323967-5 gnd rswk-swf Nichtlineare Welle (DE-588)4042102-8 gnd rswk-swf Dispersion Welle (DE-588)4150202-4 s Nichtlineare Welle (DE-588)4042102-8 s Reaktions-Diffusionsgleichung (DE-588)4323967-5 s DE-604 Lafortune, Stéphane 1958- Verfasser (DE-588)173355757 aut Manukian, Vahagn Verfasser aut Erscheint auch als Online-Ausgabe 978-1-003-14761-9 Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034073864&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ghazaryan, Anna R. Lafortune, Stéphane 1958- Manukian, Vahagn Introduction to traveling waves Dispersion Welle (DE-588)4150202-4 gnd Reaktions-Diffusionsgleichung (DE-588)4323967-5 gnd Nichtlineare Welle (DE-588)4042102-8 gnd |
| subject_GND | (DE-588)4150202-4 (DE-588)4323967-5 (DE-588)4042102-8 |
| title | Introduction to traveling waves |
| title_auth | Introduction to traveling waves |
| title_exact_search | Introduction to traveling waves |
| title_exact_search_txtP | Introduction to traveling waves |
| title_full | Introduction to traveling waves Anna R. Ghazaryan, Miami University, USA, Stéphane Lafortune, College of Charleston, USA, Vahagn Manukian, Miami University, USA |
| title_fullStr | Introduction to traveling waves Anna R. Ghazaryan, Miami University, USA, Stéphane Lafortune, College of Charleston, USA, Vahagn Manukian, Miami University, USA |
| title_full_unstemmed | Introduction to traveling waves Anna R. Ghazaryan, Miami University, USA, Stéphane Lafortune, College of Charleston, USA, Vahagn Manukian, Miami University, USA |
| title_short | Introduction to traveling waves |
| title_sort | introduction to traveling waves |
| topic | Dispersion Welle (DE-588)4150202-4 gnd Reaktions-Diffusionsgleichung (DE-588)4323967-5 gnd Nichtlineare Welle (DE-588)4042102-8 gnd |
| topic_facet | Dispersion Welle Reaktions-Diffusionsgleichung Nichtlineare Welle |
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